Giải phương trình lượng giác: $2\cos \frac{x}{2} + \sqrt 3 = 0$có nghiệm là
A. $x = \pm \frac{{5\pi }}{6} + k4\pi .$
B. $x = \pm \frac{{5\pi }}{3} + k4\pi .$
C. $x = \pm \frac{{5\pi }}{6} + k2\pi .$
D. $x = \pm \frac{{5\pi }}{3} + k2\pi .$
A. $x = \pm \frac{{5\pi }}{6} + k4\pi .$
B. $x = \pm \frac{{5\pi }}{3} + k4\pi .$
C. $x = \pm \frac{{5\pi }}{6} + k2\pi .$
D. $x = \pm \frac{{5\pi }}{3} + k2\pi .$
Chọn B.
$2\cos \frac{x}{2} + \sqrt 3 = 0$$ \Leftrightarrow \cos \frac{x}{2} = - \frac{{\sqrt 3 }}{2} \Leftrightarrow \cos \frac{x}{2} = \cos \frac{{5\pi }}{6}$$ \Leftrightarrow \frac{x}{2} = \pm \frac{{5\pi }}{6} + k2\pi \Leftrightarrow x = \pm \frac{{5\pi }}{3} + k4\pi ,\left( {k \in \mathbb{Z}} \right).$
$2\cos \frac{x}{2} + \sqrt 3 = 0$$ \Leftrightarrow \cos \frac{x}{2} = - \frac{{\sqrt 3 }}{2} \Leftrightarrow \cos \frac{x}{2} = \cos \frac{{5\pi }}{6}$$ \Leftrightarrow \frac{x}{2} = \pm \frac{{5\pi }}{6} + k2\pi \Leftrightarrow x = \pm \frac{{5\pi }}{3} + k4\pi ,\left( {k \in \mathbb{Z}} \right).$